Question: Reduce to lowest terms: $ \dfrac{1}{9} \div \dfrac{7}{6} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{7}{6}$ is $ \dfrac{6}{7}$ Therefore: $ \dfrac{1}{9} \div \dfrac{7}{6} = \dfrac{1}{9} \times \dfrac{6}{7} $ $ \phantom{ \dfrac{1}{9} \times \dfrac{6}{7}} = \dfrac{1 \times 6}{9 \times 7} $ $ \phantom{ \dfrac{1}{9} \times \dfrac{6}{7}} = \dfrac{6}{63} $ The numerator and denominator have a common divisor of $3$, so we can simplify: $ \dfrac{6}{63} = \dfrac{6 \div 3}{63 \div 3} = \dfrac{2}{21} $